don't bother going to the Alps for road biking for a few months. A lot of the higher cols will be shut for a good while. I was frozen descending in the rain in July, let alone doing similar earlier in the year.

Bourg d'Oisans (at the foot of Alpe d'Huez) has a great bike shop to hire, unfortunately it's a bit of a pig to get there in the summer if flying. You can usually only get flights to Grenoble from the UK (and bus transfer) during ski season. You could fly to Lyon and hire a car though.

I'd say your best bet would be get a flight to Geneva and go somewhere in the mountains by train or transfer (there are more transfer companies working out of Geneva). You could try one of these road bike training/guiding companies. Other option is Eurostar to Paris, transfer onto TGV to somewhere like Bourg St Maurice.

We've been over quite a few times for summer holidays, but have always driven.

Assuming you're too early for the famous passes, some lower down places:

Lake Annecy (in France) is on the edge of the Alps. The route around Annecy was a Tour de France stage, and is by no means flat, but I think it is probably about low enough that it will be possible to do before June (check that though!). Annecy has a train station (from Lyon or Geneva I think, not sure). Absolutely masses of roadies riding round there.

Also Lake Como in Italy - again not so high, unless you head off into the alps proper, but quite mountainous. Trains from Milan. There were lots of roadies there when we went years back.